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Prices of goods, services, and resources that are proportional to true opportunity costs for the economy, taking account of any externalities. If individuals and firms all made choices to maximize their pay-offs subject to a set of prices proportional to the shadow prices for the economy, the resulting equilibrium would be Pareto efficient. In a competitive economy with no market failure, market prices and shadow prices would be equivalent. In an economy with market failure, such as monopoly, legal price regulation and externalities, actual and shadow prices do not coincide. The Lagrange multipliers appearing in constrained optimization problems can be interpreted as shadow prices. See also Pareto efficiency.